Related papers: Entropy of tropical holonomic sequences
Take a multiplicative monoid of sequences in which the multiplication is given by Hadamard product. The set of linear combinations of interleaving monoid elements then yields a ring. For hypergeometric sequences, the resulting ring is a…
We review the different proposals and attempts to identify the ``horizon molecules" that would give a kinematical estimation for the black hole entropy in causal set theory. The proposals are presented according to their chronological…
We enumerate the intervals in the Tamari lattices. For this, we introduce an inductive description of the intervals. Then a notion of "new interval" is defined and these are also enumerated. A a side result, the inverse of two special…
In a previous paper a new approach has been introduced for computing, recursively and numerically, one-loop tensor integrals. Here we describe a few modifications of the original method that allow a more efficient numerical implementation…
An algorithm is designed which decomposes a tropical univariate rational function into a composition of tropical binomials and trinomials. When a function is monotone, the composition consists just of binomials. Similar algorithms are…
The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well.…
Through direct thermodynamic calculations we have shown that different classical entropies of two-dimensional extreme black holes appear due to two different treatments, namely Hawking's treatment and Zaslavskii's treatment. Geometrical and…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…
The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of products of two simplices. Applications…
The entropy of a Ba\~nados, Teitelboim, and Zanelli black hole in topologically massive gravity had been given with the form inconsistent with the Bekenstein-Hawking entropy. In the paper, we provide a consistent statistical interpretation…
The problem where a tropical cyclone intensifies dramatically within a short period of time is known as rapid intensification. This has been one of the major challenges for tropical weather forecasting. Recurrent neural networks have been…
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the…
We compute the integral third homology of most of the sporadic finite simple groups and of their central extensions.
This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become…
In this article, we study the tropical counterpart of the enumeration of rational curves in $\mathbb{CP}^2$ with first order tangency. We use the tropical analogue of the WDVV technique to compute rational tropical plane curves of degree…
We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…
We use an alternative definition of topological complexity to show that the topological complexity of the mapping telescope of a sequence $X_1\rightarrow X_2\rightarrow X_3\rightarrow...$ is bounded above by $2max{TC(X_i); i=1,2,...}$.
We extend the definition of algebraic entropy to endomorphisms of affine varieties. We calculate algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we…
We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a…
Tropical cyclone (TC) intensity forecasts are ultimately issued by human forecasters. The human in-the-loop pipeline requires that any forecasting guidance must be easily digestible by TC experts if it is to be adopted at operational…